For large system size, the adaptive time-dependent density-matrix
renormalization-group (t-DMRG) can be applied with a second order
Trotter expansion of Hamiltonian as described in
[1]}, [2]}. In order to check the accuracy of the results
of t-DMRG, the results of exact diagonalization can be considered as
a benchmark for a small size system. In the simulation, a Trotter
slicing \(\delta t=2.5\cdot 10^{-2}\)  and Matlab codes of t-DMRG with
double precision are performed with a truncated Hilbert space of
\(m=60\) . It turns out that a typically discarded weight of \(\delta \rho = 10^{-8}\)  can keep the relative error \(\delta C\)  in \(C\)  below
\(10^{-6}\)  for a chain of \(L = 60\)  sites with time \(t\le 40/J\) .
